In a single node Loewner problem one has to recover a Pick or Nevanlinna function (analytic and with positive imaginary part in the open upper half plane) when at the node the nontangential boundary limits for the function and its derivatives are prescribed. In this paper, a matrix version is analysed where finitely many of these boundary conditions are prescribed and these conditions should only hold when the solution is restricted to certain subspaces. This corresponds to a generalization of a truncated directional Nevanlinna-Pick interpolation problem where the directions are the one-dimensional subspaces where the interpolation conditions have to hold. The formulation is in terms of operators on finite dimensional Hilbert spaces. A necessary and sufficient condition for the solvability of the problem is proved to be a direct generalization of the fact that the Pick kernel for the problem has to be nonnegative. The restricted (moment matching in certain subspaces) and truncated (a finite number of moments are given) matrix valued Hamburger moment problem is discussed as a direct corollary of the previous problem. Here the necessary and sufficient condition for solvability is that the Hankel kernel is nonnegative.